document.write( "Question 268667: Hello, I am in a calculus course, and I am having difficulty solving this problem:\r
\n" ); document.write( "\n" ); document.write( "Consider the circle C1: (x-1)^2+y^2=1, and the circle C2: x^2+y^2=r^2. For small r values, the circles intersect. Consider the line that goes through the top of C2 and the intersection point in quadrant 1. As r->0, where does the root of the line tend to?\r
\n" ); document.write( "\n" ); document.write( "Thank you for the help!\r
\n" ); document.write( "\n" ); document.write( "J \n" ); document.write( "
Algebra.Com's Answer #196889 by drk(1908)\"\" \"About 
You can put this solution on YOUR website!
OUr two equations are
\n" ); document.write( "(i) \"%28x-1%29%5E2+%2B+y%5E2+=+1\"
\n" ); document.write( "(ii) \"x%5E2+%2B+y%5E2+=+r%5E2\"
\n" ); document.write( "take (i) - (ii) to get
\n" ); document.write( "(iii) \"%28x-1%29%5E2+-+x%5E2+=+1+-+r%5E2\"
\n" ); document.write( "simplify to get
\n" ); document.write( "(iv) \"-2x+%2B+1+=+1+-+r%5E2\"
\n" ); document.write( "solving for x we get
\n" ); document.write( "(v) \"r+%5E2%2F2\"
\n" ); document.write( "now, we can find y as
\n" ); document.write( "(vi) y = \"sqrt%28r%5E2+-+%28r%5E4%2F4%29%29\"
\n" ); document.write( "or simplified to
\n" ); document.write( "(vii) y = \"%28r%2F2%29%2Asqrt%281-r%5E2%29\"
\n" ); document.write( "Now, the y -intercept of C2 is (0,r).
\n" ); document.write( "---
\n" ); document.write( "Next we create an equation of a line passing through the y intercept of C2 and the crossing point of the two circles as
\n" ); document.write( "(viii) y = \"%28%28-2%2B2%2Asqrt%281-r%5E2%29%29%2Fr%29X+%2B+r\"
\n" ); document.write( "We want the x intercept or the value of x when y = 0.
\n" ); document.write( "This is
\n" ); document.write( "(ix) x = \"-r%5E2%2F%28-2%2B2%2Asqrt%281-r%5E2%29%29\"
\n" ); document.write( "The limit of x as r -> 0, is 1
\n" ); document.write( "The root of the line tends to 1. \n" ); document.write( "
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